Regular and Singular Dislocations
The theory of continuous distributions of dislocations and other material defects, when formulated in terms of differential forms, is shown to comprise also the discrete, or singular, counterpart, in which defects are concentrated on lower dimensional reg
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Reuven Segev Marcelo Epstein Editors
Geometric Continuum Mechanics
Advances in Mechanics and Mathematics Advances in Continuum Mechanics Volume 42
Series Editors Paolo Maria Mariano, University of Florence Richard D. James, University of Minnesota Constantine Dafermos, Brown University
More information about this subseries at http://www.springer.com/series/16097
Reuven Segev • Marcelo Epstein Editors
Geometric Continuum Mechanics
Editors Reuven Segev Department of Mechanical Engineering Ben-Gurion University of the Negev Beer-Sheva, Israel
Marcelo Epstein Department of Mechanical and Manufacturing Engineering University of Calgary Calgary, AB, Canada
ISSN 1571-8689 ISSN 1876-9896 (electronic) Advances in Mechanics and Mathematics ISSN 2524-4639 ISSN 2524-4647 (electronic) Advances in Continuum Mechanics ISBN 978-3-030-42682-8 ISBN 978-3-030-42683-5 (eBook) https://doi.org/10.1007/978-3-030-42683-5 Mathematics Subject Classification (2020): 74A05, 74A10, 74A99, 58D15, 22A22, 58A25, 58A30 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Geometric Continuum Mechanics
This volume contains a compilation of extended articles on the applications of various topics in modern differential geometry to the foundations of continuum mechanics. The application of differential geometry to the mechanics of systems having a finite number of degrees of freedom, as appeared initially in the works of Abraham, Marsden, Souriau, Arnold, Smale, and others, and led to the vast literature that followed, needs no introduction
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